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人気のある微分積分 >

integral of 54.0595e^{sqrt(x)}x

解

\int 54.0595 e^{x} x d x

解

108.119 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x}))) + C

解答ステップ

\int 54.0595 e^{x} x d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 54.0595 \cdot \int e^{x} x d x

u置換積分法を適用する

= 54.0595 \cdot \int 2 e^{u} u^{3} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 54.0595 \cdot 2 \cdot \int e^{u} u^{3} d u

部分積分を適用する

= 54.0595 \cdot 2 (u^{3} e^{u} - \int 3 u^{2} e^{u} d u)

\int 3 u^{2} e^{u} d u = 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u}))

= 54.0595 \cdot 2 (u^{3} e^{u} - 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u})))

代用を戻す

u = x

= 54.0595 \cdot 2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x})))

簡素化

54.0595 \cdot 2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x}))) : 108.119 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

= 108.119 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

定数を解答に追加する

= 108.119 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x}))) + C

グラフ

人気の例

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